Hummingbirds have brilliant color; their
feathers have a metallic sheen that is remarkable and unique.

The following text is from
Paul A. Johnsgard's book, The Hummingbirds of North America (1997, second
edition, published by Smithsonian Institution Press in Washington, DC.) It is used with the permission of the publisher and the author.

The highly iridescent feathers of the
hummingbird gorgets are among the most specialized of all bird
feathers. But even in the male's gorget ... only about the distal
third of each feather
is modified for iridescence; the close overlapping of adjacent feathers thus generates the
unbroken color effect. The iridescence is produced by the proximal part of
the barbules, which are smooth, flattened and lack hook-like barbicels
or hamuli. Beyond the color-producing portion, the barbule is strongly narrowed and curved
toward the distal tip of the feather. The barbicels in this area help to hold together the
barbules on the side of the barb, but do not unite the barbules of adjacent barbs.
(Aldrich,1956).

...The colors do not directly depend on selective pigment absorption and
reflection, as do brown and blacks produced by the melanin pigments of non-iridescent
feathers. Rather, they depend on interference coloration, such as that resulting from the
colors seen in an oil film or soap-bubble. Basically, the colors depend on light being
passed through a substance with a different refractive index than air (1.0), and being
partially reflected back again at a second interface. The percentage of light that is
reflected back increases with the difference in the refractive indices of the two media;
in addition, the thickness of the film through which the light is passed strongly
influences the wavelengths of light that are reflected back. Put simply, red wavelengths are longer
than those at the violet end of the spectrum and generally require films that are thicker
or have higher refractive indices than those able to refract bluish or violet light. Thus,
the optimum refractive index for red feathers is about 1.85; for blue feathers it is about
1.5.

Hummingbird feathers may attain any refractive index within this range because the
iridescence portions of the barbules are densely packed with tiny, tightly packed layers
of platlets. These platlets are only about 2.5 microns in length and average about 0.18 microns in
thickness, but they vary in thickness and are differentially filled with air bubbles. The
platlets matrix, probably of melanin, evidently has a refractive index of about 2.2,
whereas the air bubbles inside have a refractive index of 1.0. Varying the amount of air
in the platlets provides a composite refractive index that ranges from the red end of the
spectrum (1.85) to the blue (1.5)....

Thus, the actual thickness of the platlets not only significantly
determines the quality of the perceived light, but it also affects the amount of air held
within the pigment granules and the consequent variations in interference effects.
Further, a
single pigment granule can produce different color effects according to the angle at which
it is viewed. When an optical film is viewed from about, it reflects longer wavelengths
than when viewed from angles progressively farther away from the perpendicular. Thus, a
gorget may appear ruby red when seen with a beam of light coming from directly behind the
eye, but as the angle is changed the gorget color will shift from red to blue and finally
to black, as the angle of incidence increases (Greenwalt, 1960a).

In hummingbirds, the color-producing pigment platlets are closely packed into a mosaic surface,
and 8 to10
such layers are then tightly stacked on top of one another in typical iridescent feathers.
Far from confusing the visual effects, such stacking actually tends to intensify and
purify the resulting spectral color, which is why hummingbirds have possibly the most
intensively iridescent feathers known in birds (Greenwalt, 1960a).

Johnsgard's sources:

Greenwalt, C.H.(1960), Hummingbirds.
Doubleday and the American Museum of Natural History, Garden City.